To belay is to secure or hold the end of a climbing rope so that the climber won't fall far if she slips. Your friend might climb a rock wall first, while you belay for her.
You can belay on your own by fixing the end of your rope, but it's more common — and safer — to have a partner belay for you while you climb. To do this, she exerts friction on the rope when you don't move, and releases more rope when you need it to climb higher. The word was first used by sailors in the 16th century, in a similar way — to secure a marine rope by coiling it around a pin.